Remarks on a Multivariate Transformation
01 Sep 1952-Annals of Mathematical Statistics (Institute of Mathematical Statistics)-Vol. 23, Iss: 3, pp 470-472
About: This article is published in Annals of Mathematical Statistics.The article was published on 1952-09-01 and is currently open access. It has received 2735 citations till now. The article focuses on the topics: Transformation (function).
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02 Jan 2013
TL;DR: In this paper, the authors provide a detailed description of the basic properties of optimal transport, including cyclical monotonicity and Kantorovich duality, and three examples of coupling techniques.
Abstract: Couplings and changes of variables.- Three examples of coupling techniques.- The founding fathers of optimal transport.- Qualitative description of optimal transport.- Basic properties.- Cyclical monotonicity and Kantorovich duality.- The Wasserstein distances.- Displacement interpolation.- The Monge-Mather shortening principle.- Solution of the Monge problem I: global approach.- Solution of the Monge problem II: Local approach.- The Jacobian equation.- Smoothness.- Qualitative picture.- Optimal transport and Riemannian geometry.- Ricci curvature.- Otto calculus.- Displacement convexity I.- Displacement convexity II.- Volume control.- Density control and local regularity.- Infinitesimal displacement convexity.- Isoperimetric-type inequalities.- Concentration inequalities.- Gradient flows I.- Gradient flows II: Qualitative properties.- Gradient flows III: Functional inequalities.- Synthetic treatment of Ricci curvature.- Analytic and synthetic points of view.- Convergence of metric-measure spaces.- Stability of optimal transport.- Weak Ricci curvature bounds I: Definition and Stability.- Weak Ricci curvature bounds II: Geometric and analytic properties.
5,524 citations
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18 Feb 1993
TL;DR: In this paper, the authors present a set of programs that summarize data with histograms and other graphics, calculate measures of spatial continuity, provide smooth least-squares-type maps, and perform stochastic spatial simulation.
Abstract: Thirty-seven programs that summarize data with histograms and other graphics, calculate measures of spatial continuity, provide smooth least-squares-type maps, and perform stochastic spatial simulation.
4,301 citations
TL;DR: This article analyses the recently suggested particle approach to filtering time series and suggests that the algorithm is not robust to outliers for two reasons: the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution.
Abstract: This article analyses the recently suggested particle approach to filtering time series. We suggest that the algorithm is not robust to outliers for two reasons: the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution. Here we tackle the first of these problems.
2,608 citations
Cites background from "Remarks on a Multivariate Transform..."
...distributed on the 0,1 interval ( Rosenblatt (1952) )....
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TL;DR: In this paper, Markov chain Monte Carlo sampling methods are exploited to provide a unified, practical likelihood-based framework for the analysis of stochastic volatility models, and a highly effective method is developed that samples all the unobserved volatilities at once using an approximate offset mixture model, followed by an importance reweighting procedure.
Abstract: In this paper, Markov chain Monte Carlo sampling methods are exploited to provide a unified, practical likelihood-based framework for the analysis of stochastic volatility models. A highly effective method is developed that samples all the unobserved volatilities at once using an approximating offset mixture model, followed by an importance reweighting procedure. This approach is compared with several alternative methods using real data. The paper also develops simulation-based methods for filtering, likelihood evaluation and model failure diagnostics. The issue of model choice using non-nested likelihood ratios and Bayes factors is also investigated. These methods are used to compare the fit of stochastic volatility and GARCH models. All the procedures are illustrated in detail.
1,892 citations
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01 Jun 1996TL;DR: Partial Safety Factor Method Probabilistic Information Simple Reliability Index Geometricreliability Index Generalized Reliability index Transformation Sensitivity Analysis Monte Carlo Methods Load Combinations Statistical and Model Uncertainty Decision Philosophy Reliability of Existing Structures System Reliability Analysis.
Abstract: Partial Safety Factor Method Probabilistic Information Simple Reliability Index Geometric Reliability Index Generalized Reliability Index Transformation Sensitivity Analysis Monte Carlo Methods Load Combinations Statistical and Model Uncertainty Decision Philosophy Reliability of Existing Structures System Reliability Analysis Introduction to Process Descriptions.
1,852 citations